Wedged optical flats, which are useful for such purposes as windows for lasers, output couplers, and beam splitters, are typically fabricated to required tolerances for finish, flatness, and wedge angle on loose-abrasive lapping machines. One or more of the optical flats are mounted between relatively rotating finishing plates in the presence of a loose abrasive. One side of the plates is weighted to fashion the desired wedge angle. While single batches of optical flats can be finished to desired tolerances, the process is operator-dependent and generally unrepeatable.